Implantable bioelectronic devices predominantly use wireless links for communication and/or power transfer. When considering transmitting implanted antennas, electromagnetic radiation through biological media is highly attenuated, and previous work has shown that the in-body path loss can be separated into three parts: the losses incurred by the propagating fields, the reflections at media interfaces, and the coupling of the antenna reactive near field and the lossy body. The first two are unavoidable, but a careful antenna design should minimize the near-field losses. Thus, quantifying the near-field losses of implanted antennas is useful in selecting the antenna topology for preliminary design. The aim of this paper is to present a simplified model of an implanted antenna that provides closed-form approximate expressions to estimate EM radiation from the implant. In particular, we extend the expressions for the reactive near-field losses to both deep and shallow implants, by taking into account the implantation depth. Additionally, the proposed approximate method is verified by comparing the results obtained with the full-wave simulations in the case of a miniature implanted antenna, and with both simulated and measured results from two practical examples found in the literature.